D-Sequence Edge Binomials, and Regularity of Powers of Binomial Edge Ideals of Trees

TL;DR

This paper characterizes when edge-binomials of trees form a d-sequence based on degree sequences and investigates the regularity of powers of binomial edge ideals generated by these sequences.

Contribution

It provides necessary and sufficient conditions for edge-binomials to form a d-sequence in trees and analyzes the regularity of their powers.

Findings

Characterization of d-sequence edge-binomials in trees

Conditions linking degree sequences to d-sequences

Results on the regularity of powers of binomial edge ideals

Abstract

We provide the necessary and sufficient conditions for the edge-binomials of the tree forming a $d$-sequence in terms of the degree sequence notion of a graph. We study the regularity of powers of the binomial edge ideals of trees generated by $d$-sequence edge binomials.